Label
Class
Class size
Class degree
Base field
Field degree
Field signature
Conductor
Conductor norm
Discriminant norm
Root analytic conductor
Bad primes
Rank
Torsion
CM
CM
Sato-Tate
$\Q$-curve
Base change
Semistable
Potentially good
Nonmax $\ell$
mod-$\ell$ images
$Ш_{\textrm{an}}$
Tamagawa
Regulator
Period
Leading coeff
j-invariant
Weierstrass coefficients
Weierstrass equation
49.2-a1
49.2-a
$2$
$7$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
49.2
\( 7^{2} \)
\( - 7^{7} \)
$1.72118$
$(-a-2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$7$
7B.6.3
$1$
\( 2 \)
$4.195650442$
$1.068764585$
2.463788418
\( -\frac{195338235078135808}{7} a - \frac{613353587397607424}{7} \)
\( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( -7698 a - 29615\) , \( 842473 a + 2486905\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-7698a-29615\right){x}+842473a+2486905$
49.2-a2
49.2-a
$2$
$7$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
49.2
\( 7^{2} \)
\( - 7^{13} \)
$1.72118$
$(-a-2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$7$
7B.6.1
$1$
\( 2 \)
$0.599378634$
$7.481352100$
2.463788418
\( -\frac{1840001024}{823543} a + \frac{7615438848}{823543} \)
\( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( 2 a - 5\) , \( 16 a + 57\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a-5\right){x}+16a+57$
49.2-b1
49.2-b
$2$
$7$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
49.2
\( 7^{2} \)
\( - 7^{9} \)
$1.72118$
$(-a-2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$7$
7B
$1$
\( 2 \)
$1.501562525$
$2.678376117$
2.209718956
\( -68910804992 a + 285294501888 \)
\( \bigl[0\) , \( -1\) , \( a + 1\) , \( -232 a - 746\) , \( 3993 a + 12514\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-232a-746\right){x}+3993a+12514$
49.2-b2
49.2-b
$2$
$7$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
49.2
\( 7^{2} \)
\( - 7^{3} \)
$1.72118$
$(-a-2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$7$
7B
$1$
\( 2 \)
$0.214508932$
$18.74863282$
2.209718956
\( -4096 a + 16384 \)
\( \bigl[0\) , \( -1\) , \( a + 1\) , \( -2 a - 6\) , \( -6 a - 20\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-2a-6\right){x}-6a-20$
49.2-c1
49.2-c
$2$
$7$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
49.2
\( 7^{2} \)
\( - 7^{3} \)
$1.72118$
$(-a-2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$7$
7B.2.3
$1$
\( 2 \)
$1.635744836$
$2.274807683$
2.044477338
\( -68910804992 a + 285294501888 \)
\( \bigl[0\) , \( a\) , \( a + 1\) , \( -4 a - 23\) , \( -25 a - 86\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-4a-23\right){x}-25a-86$
49.2-c2
49.2-c
$2$
$7$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
49.2
\( 7^{2} \)
\( - 7^{9} \)
$1.72118$
$(-a-2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$7$
7B.2.1
$1$
\( 2 \)
$0.233677833$
$15.92365378$
2.044477338
\( -4096 a + 16384 \)
\( \bigl[0\) , \( -a\) , \( a + 1\) , \( 25 a - 98\) , \( -99 a + 401\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(25a-98\right){x}-99a+401$
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*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.